Logical Frameworks as a Basis for Verification Tools: A Case Study

Abstract

Wide-spread acceptance and use of formal methods in software development hinges on the availability of powerful tools. Tools must be both reliable and offer real assistance to the user. Logical frameworks are a suitable medium to build such tools, since they provide a means to show the faithfulness and adequacy of the implementation, and at the same time provide the flexibility needed to build sufficiently automated tools. We present Z-in-Isabelle, a deep semantic embedding of the specification language Z and a deductive system for Z in the generic theorem prover Isabelle. Z is based on Zermelo-Fraenkel set theory and first-order predicate logic, extended by a notion of schemas. Isabelle supports a fragment of higher-order predicate logic, in which object logics such as Z can be encoded as theories. We illustrate the use of Z-in-Isabelle with a data refinement proof. We assess to what extent such proofs need to and can be automated to make implementations in logical frameworks such as Z-in-Isabelle viable tools for reasoning about specifications.